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NDA 2022
Exam
NDA
Year
2022
Subject
Mathematics
Chapter
Limits

NDA 2022 · Mathematics · Limits

What is _ h arrow 0 ( ^2(x+h)- ^2 x)/(h) equal to?

What is lim⁡h→0sin⁡2(x+h)−sin⁡2xh\lim _{h \rightarrow 0} \frac{\sin ^2(x+h)-\sin ^2 x}{h} equal to?

Options

  1. Asin⁡2x\sin ^2 x
  2. Bcos⁡2x\cos ^2 x
  3. Csin⁡2x\sin 2 x
  4. Dcos⁡2x\cos 2 x

Correct answer

C. sin⁡2x\sin 2 x

Step-by-step solution

lim⁡h→0sin⁡2(x+h)−sin⁡2xh\lim _{h \rightarrow 0} \frac{\sin ^2(x+h)-\sin ^2 x}{h} Apply L' Hospital rule lim⁡h→02sin⁡(x+h)⋅cos⁡(x+h)=2sin⁡x⋅cos⁡x\lim _{h \rightarrow 0} 2 \sin (x+h) \cdot \cos (x+h)=2 \sin x \cdot \cos x [Take xx as constant] =sin⁡2x=\sin 2 x
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